Can I play Fizz then equip him with Last Rites before his ability plays?

No, you cannot play Fizz, Trickster and then equip him with Last Rites before his "When you play me" triggered ability resolves.

The Reasoning

When you play a unit, it enters the chain as a pending item. Once it finalizes and enters the battlefield, its "When you play me" (WYPM) ability triggers and is added to the chain.

According to Rule 381 and Rule 377.3, activated abilities (like the [Equip] ability on Last Rites) can only be activated during an Open State on your turn. Because Fizz's triggered ability is currently on the chain, the game state is Closed. In a Closed State, only [Reaction] cards or abilities can be played or activated. Since the [Equip] ability on Last Rites is a standard activated ability and not a [Reaction], it cannot be activated while the chain is occupied by Fizz's triggered ability.

The Sequence

1. Play Fizz: You play Fizz, Trickster from your hand. He enters the chain as a pending item.
2. Fizz Enters Play: Fizz finalizes and enters the battlefield.
3. WYPM Trigger: Fizz's "When you play me" ability triggers and is added to the chain. The state is now Closed.
4. Priority: Because the state is Closed, you cannot activate the [Equip] ability of Last Rites. You must either pass priority or play a [Reaction].
5. Resolution: If both players pass, the chain resolves. Fizz's ability executes, allowing you to play a spell from your trash. Only after this ability has fully resolved and the chain is empty (returning the game to an Open State) could you then activate the [Equip] ability of Last Rites.

This is my interpretation based on the interaction between triggered abilities, the chain, and the requirements for activating abilities (Rule 381). No official FAQ exists for this specific interaction.